Past exam of the mathematical methods II course of the University of Oxford / 2018 / 9 / b / Solution

Use the vector triple product identity:For the $i$th component of the second integral, the antisymmetric first moment of a localized solenoidal field with $C^{\prime }=e_i$ gives ${\int }_V{r}_i(C\cdot J)dV=-{\int }_V(C\cdot r)J_{i}dV$. Thus the two terms on the right have opposite integrals. Consequently